### "Heat Equation Derivative Formulas for Vector Bundles," by B. Driver and Anton Thalmaier.

(UCSD and Univ. of Bonn Preprint, March 2000, and  1998 )

Available as a DVI file (284K) or a PDF file (769K).

Abstract

We use martingale methods to give Bismut type derivative formulas
for differentials and co-differentials of heat semigroups on forms, and more
generally for sections of vector bundles. The formulas are mainly in terms
of Weitzenb\"{o}ck curvature terms, in most cases derivatives of the
curvature are not involved. In particular, our results improve the formula
in Driver \cite{Driver:97b} for logarithmic derivatives of the heat kernel
measure on a Riemannian manifold. Our formulas also include the formulas in
Elworthy and Li \cite{Elworthy-Li:98}.

March 2000

 08/15/2016 02:53 PM